Subgroups — C₅×#66635 #13132335

Order 1680.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₄₂	C₂	1	1	yes	maximal, characteristic
3	C₅×C₃⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₅×#1144	—	3	1	no	maximal, Hall
5	C₃×C₄×C₅×C₇	—	2	1	no	—
6	C₃×C₄×C₅×C₇	C₂²	1	1	yes	characteristic
7	C₅×Dic₂₁	—	2	1	no	—
8	#66635	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₇×Q₈	D₃	1	1	yes	characteristic
10	C₅×Dic₁₄	—	3	1	no	—
11	C₅×C₇⋊C₈	—	3	1	no	—
12	C₅×#216	—	7	1	no	maximal, Hall
13	C₂×C₃×C₅×C₇	D₄	1	1	yes	characteristic
14	C₃×C₇×Q₈	C₂×C₅	1	1	yes	characteristic
15	Dic₄₂	C₂×C₅	1	1	yes	characteristic
16	C₃⋊(C₇⋊C₈)	C₂×C₅	1	1	yes	characteristic
17	C₄×C₅×C₇	—	2	1	no	—
18	C₄×C₅×C₇	C₂×D₃	1	1	yes	characteristic
19	C₅×Dic₇	—	6	1	no	—
20	C₃×C₅×Q₈	D₇	1	1	yes	characteristic
21	C₅×Dic₆	—	7	1	no	—
22	C₅×C₃⋊C₈	—	7	1	no	—
23	#1144	—	3	1	no	Hall
24	C₃×C₅×C₇	Q₁₆	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄×C₇	—	2	1	no	—
26	C₃×C₄×C₇	C₂²×C₅	1	1	yes	characteristic
27	Dic₂₁	—	2	1	no	—
28	C₅×Q₁₆	—	21	1	no	Hall
29	C₂×C₅×C₇	#67	1	1	yes	characteristic
30	C₃×C₄×C₅	—	2	1	no	—
31	C₃×C₄×C₅	C₂×D₇	1	1	yes	characteristic
32	C₅×Dic₃	—	14	1	no	—
33	C₇×Q₈	C₅×D₃	1	1	yes	characteristic
34	Dic₁₄	—	3	1	no	—
35	C₇⋊C₈	—	3	1	no	—
36	#216	—	7	1	no	Hall
37	C₂×C₃×C₇	C₅×D₄	1	1	yes	characteristic
38	C₅×Q₈	—	21	1	no	—
39	C₅×Q₈	D₂₁	1	1	yes	characteristic
40	C₅×C₈	—	21	1	no	—
41	C₅×C₇	#216	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₅	C₂²⋊D₇	1	1	yes	characteristic
43	C₄×C₇	—	2	1	no	—
44	C₄×C₇	C₂×C₅×D₃	1	1	yes	characteristic
45	Dic₇	—	6	1	no	—
46	C₃×Q₈	C₅×D₇	1	1	yes	characteristic
47	Dic₆	—	7	1	no	—
48	C₃⋊C₈	—	7	1	no	—
49	C₃×C₇	C₅×Q₁₆	1	1	yes	characteristic, complemented, Hall
50	C₄×C₅	—	2	1	no	—
51	C₄×C₅	—	42	1	no	—
52	C₄×C₅	C₂×D₂₁	1	1	yes	characteristic
53	Q₁₆	—	21	1	no	Sylow
54	C₃×C₅	#1144	1	1	yes	characteristic, complemented, Hall
55	C₂×C₇	C₅×#67	1	1	yes	characteristic
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	C₂×C₅×D₇	1	1	yes	characteristic
58	Dic₃	—	14	1	no	—
59	C₂×C₅	#4268	1	1	yes	characteristic
60	Q₈	—	21	1	no	—
61	Q₈	C₅×D₂₁	1	1	yes	characteristic
62	C₈	—	21	1	no	—
63	C₇	C₅×#216	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	C₅×C₂²⋊D₇	1	1	yes	characteristic
65	C₅	#66635	1	1	yes	characteristic, direct product factor, Sylow
66	C₄	—	2	1	no	—
67	C₄	—	42	1	no	—
68	C₄	C₂×C₅×D₂₁	1	1	yes	characteristic
69	C₃	C₅×#1144	1	1	yes	characteristic, complemented, Sylow
70	C₂	C₅×#4268	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#4268
commutator, cosocle	C₃×C₄×C₇	C₂²×C₅
Frattini	C₄	C₂×C₅×D₂₁
Fitting	C₃×C₅×C₇×Q₈	C₂
socle, prime radical	C₂×C₃×C₅×C₇	D₄
hypercenter	C₅×Q₈	D₂₁
hypocenter	C₃×C₇	C₅×Q₁₆
LCS	G ▷ C₃×C₄×C₇ ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
8. #66635	C₅	direct (N × H)
24. C₃×C₅×C₇	Q₁₆	semidirect
41. C₅×C₇	#216	semidirect
49. C₃×C₇	C₅×Q₁₆	semidirect
54. C₃×C₅	#1144	semidirect
63. C₇	C₅×#216	semidirect
65. C₅	#66635	direct (N × H)
69. C₃	C₅×#1144	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₇×Q₈	2
C₅×Dic₄₂	2
C₅×C₃⋊(C₇⋊C₈)	2
C₅×#1144	3
#66635	5
C₅×#216	7

Subgroups — C5×#66635 #13132335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66635 #13132335